Exporting / Rendering in a Print-Ready Format - I'm Stuck!
People at print shops expect most illustration, desktop publishing and page layout graphics design work to be handed in a vector format like say PDF, commonly also EPS, Adobe Illustrator, Coreldraw, Indesing, and to a lesser extent even SVG.

The advantage of these vector graphics formats is that they don't pixelate when zoomed in on, so they provide a theoretically infinite quality and definition. They can also be much smaller in file size for higher image quality levels. 

And for much of your work it does look like it could be made in a vector graphics editors, like say Inkscape, CorelDraw, Adobe Illustrator, Indesign, etc.
Logo designs usually benefit from vector formats, so does page layout like fliers, posters, advertising.

That being said not all stuff can be done in vector graphics, images, photos, renderings, and elements with many color variations benefit from raster graphics file formats like JPG, TIFF, PNG, TGA, HDR, etc..

Renderings from 3D models are among those that are generally represented by raster images. These can and should be combined with the remaining vector elements in a mixed document whenever possible. 
While it is possible to extract vector drawings from 3D models directly, it is quite more limited in terms of representation, and not trivial to achieve.

Under Blender you have a few options, which is using Freestyle which is implemented as a rendering engine that allows extracting non-photorealistic images. There is one plugin shipped with Blender by default that allows exporting SVG from freestyle.

One other option under Blender is using the third party addon SVG Output Script, which while more basic at times, allows viewport exports that may produce closer to expected output for certain situations. 

You can also look into NURBS modelling applications like Rhino or Moi that have math based geometries and allow more accurate vector output in PDF format.

You can then import those into any vector graphics editor and tweak it further.

Have in mind that non of these options aim to export a fully realistic raytraced image of your model, like traditional rendering, quality may also vary. Most of the time though, a high enough quality rendering, with dense enough resolution images should suffice even for printing, if correctly combined with vector info for all non 3D elements.

For purely bidimensional graphics like most of the logos, they are likely right, you should probably change your workflow and use proper drafting tools like say free and open source Inkscape, or Scribus.

I see no good reason (other than enjoying your current workflow) for doing basic 2D graphic design in a fully 3D workflow. It is more complex and doesn't really provide any benefit.